A couple of the new national polls out today point to a lot of Dems who seem to think Hillary Clinton would be a fine running mate. The latest numbers from Gallup point to a majority of rank-and-file Dems who like the idea of an Obama/Clinton ticket.

A new Gallup poll shows 55 percent of Democrats and Democratic-leaning independents surveyed think Obama should offer the New York senator a spot on his ticket. That number is significantly influenced by Clinton’s supporters — close the 75 percent of her backers want the No. 2 spot to be offered, while only 43 percent of Obama supporters feel the same.

The poll comes as some of Clinton’s highest profile backers increasingly suggest Obama and Clinton should team up for the general election. Speaking in New York Friday, Sen. Chuck Schumer said he at first didn’t think such a team was possible but now believes “it could be.”

In the new WaPo/ABC poll, Dems were given an open-ended question about a possible Obama running mate, and about four in 10 named Clinton as their choice, followed by John Edwards, who drew 10%. (The Post added, “[M]ost Americans, including a slim majority of Democrats, said putting Clinton on the ticket would not have much effect on their vote in November.”)

I don’t doubt that Clinton enjoys an enormous base of support within the party. That should be pretty obvious — she’s won more 15 million Democratic votes at this point. For her most enthusiastic supporters, having Clinton on the ticket, even in the #2 slot, might very well be better than nothing.

But I thought I’d take a minute to note that polls about running mates don’t mean a whole lot.

I went back and started poking through polls from the 2000 race, shortly after Bush and Gore had effectively secured their respective party’s nomination. Asked who the candidates should pick for their tickets, a Zogby poll from March 2000 showed Bill Bradley as the top choice for Dems, followed by former Senate Majority Leader George Mitchell. Republicans in the poll were nearly tied between Elizabeth Dole and John McCain. A few weeks later, a Fox News poll showed similar results, with Bradley and McCain getting pluralities. In May 2000, an NBC/WSJ poll found the same thing.

Four years later, Dems were asked in the spring of 2004 who John Kerry should pick for the Democratic ticket. Most polls showed John Edwards as the clear favorite, with Hillary Clinton coming in second in several polls. (Wesley Clark and Howard Dean also fared pretty well in these polls.)

I think you see where I’m going with this. These VP polls tend to measure name recognition — and most VP candidates aren’t well known to a national audience. Before 2000, I suspect most Republicans were not at all familiar with Dick Cheney, but then they got to know him pretty quickly. The same was true of Joe Lieberman.

I did a radio show the other day, and mentioned some names of people I thought Obama might consider, including Sebelius, Webb, Strickland, Sherrod Brown, and Napolitano. I was talking to some pretty well-informed people, but of the group, only Webb’s name was familiar. If they were polled with an open-ended question, these names wouldn’t have come up at all.

The point isn’t whether Clinton would be a good choice for Obama or not; that’s a separate matter. The point is these VP polls don’t tell us a whole lot. Obama may very well pick a running mate who isn’t nationally known, but I suspect we’d all get to know him or her pretty quickly.